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The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We…
We analyse quantile temporal-difference learning (QTD), a distributional reinforcement learning algorithm that has proven to be a key component in several successful large-scale applications of reinforcement learning. Despite these…
We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…
Quantum dot (QD) solids are promising optoelectronic materials; further advancing their device functionality depends on understanding their energy transport mechanisms. The commonly invoked near-field F\"orster resonance energy transfer…
In this paper, a two-sided variable-coefficient space-fractional diffusion equation with fractional Neumann boundary condition is considered. To conquer the weak singularity caused by nonlocal space-fractional differential operators, a…
Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
Federated learning (FL) is a promising technology that enables edge devices/clients to collaboratively and iteratively train a machine learning model under the coordination of a central server. The most common approach to FL is first-order…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…
Quantum key distribution (QKD) is the fastest-growing and relatively mature technology in the field of quantum information, enabling information-theoretically secure key distribution between two remote users. Although QKD based on…
We consider a continuous-variable (CV) quantum key distribution (QKD) protocol over free-space channels, which is simpler and more robust than typical CV QKD protocols. It uses a bright laser, squeezed and modulated in the amplitude…
We propose and analyse a spatial discretization of the non-local Quantum Drift Diffusion (nlQDD) model by Degond, M\`{e}hats and Ringhofer in one space dimension. With our approach, that uses consistently matrices on ${\mathbb C}^N$ instead…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional…
Within QED, we examine several issues related to constructing a parton-model-based QCD transport theory. We rewrite the QED analog of the parton model, the Weizsaecker-Williams Approximation, entirely in terms of phase-space quantities and…
We present a novel method for diffusion-guided frameworks for view-consistent super-resolution (SR) in neural rendering. Our approach leverages existing 2D SR models in conjunction with advanced techniques such as Variational Score…
This paper studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker-Planck equations for QSDs. Similar as the case of Fokker-Planck equations for invariant…
Quality-Diversity (QD) algorithms constitute a branch of optimization that is concerned with discovering a diverse and high-quality set of solutions to an optimization problem. Current QD methods commonly maintain diversity by dividing the…